Toy

## 
## INLA-IS
## 
## Posterior means:
## [1]  0.9301271 -0.9880918
## 
## Posterior covariance:
##              [,1]         [,2]
## [1,]  0.132599816 -0.004151681
## [2,] -0.004151681  0.130064375
## 
## Sample size (to estimate the mean)
## [1] 9137.7
## 
## Sample size (to estimate the variance)
## [1] 3675.384
## 
## Sample size (to estimate the kurtosis)
## [1] 5893.742
## 
## L2 discrepancy
## [1] 0.003071926
## 
## Sample size (per variable)
## [1] 8124.978 7555.027
## 
## INLA-AMIS
## 
## Posterior means:
## [1]  0.9354200 -0.9824848
## 
## Posterior covariance:
##              [,1]         [,2]
## [1,]  0.128952952 -0.005238025
## [2,] -0.005238025  0.132484218
## 
## Sample size (to estimate the mean)
## [1] 9618.056
## 
## Sample size (to estimate the variance)
## [1] 9087.699
## 
## Sample size (to estimate the kurtosis)
## [1] 9265.605
## 
## L2 discrepancy
## [1] 0.001992765
## 
## Sample size (per variable)
## [1] 8510.857 8476.343

Lasso

## 
## INLA-IS
## 
## Posterior means:
## [1] -0.08856204  0.26010748  0.08248470  0.09992697  0.01505261
## 
## Posterior covariance:
##               [,1]         [,2]          [,3]          [,4]          [,5]
## [1,]  0.0021179696 -0.001089102 -0.0011607633  8.846117e-04 -1.107666e-03
## [2,] -0.0010891018  0.004282455  0.0017398917 -1.402262e-03 -1.391188e-03
## [3,] -0.0011607633  0.001739892  0.0012629344 -8.978626e-04 -1.483391e-04
## [4,]  0.0008846117 -0.001402262 -0.0008978626  6.890096e-04  8.521568e-05
## [5,] -0.0011076656 -0.001391188 -0.0001483391  8.521568e-05  1.712434e-03
## 
## Sample size (to estimate the mean)
## [1] 3.714073
## 
## Sample size (to estimate the variance)
## [1] 1.515723
## 
## Sample size (to estimate the kurtosis)
## [1] 1.655757
## 
## L2 discrepancy
## [1] 0.518793
## 
## Sample size (per variable)
## [1] 4.232757 3.655277 4.726924 2.982445 5.031430
## 
## INLA-AMIS
## 
## Posterior means:
## [1] -0.007289224  0.168143956  0.028726525  0.073246574  0.202813278
## 
## Posterior covariance:
##               [,1]         [,2]          [,3]          [,4]          [,5]
## [1,]  0.0065593662 -0.004448723  0.0001756576 -0.0008563857 -0.0010981170
## [2,] -0.0044487235  0.013241012  0.0014917896 -0.0042806420 -0.0046288830
## [3,]  0.0001756576  0.001491790  0.0044565013 -0.0007320848 -0.0043702715
## [4,] -0.0008563857 -0.004280642 -0.0007320848  0.0071316218 -0.0009105724
## [5,] -0.0010981170 -0.004628883 -0.0043702715 -0.0009105724  0.0116082610
## 
## Sample size (to estimate the mean)
## [1] 4321.355
## 
## Sample size (to estimate the variance)
## [1] 1855.853
## 
## Sample size (to estimate the kurtosis)
## [1] 2414.679
## 
## L2 discrepancy
## [1] 0.01146337
## 
## Sample size (per variable)
## [1] 2575.034 2884.157 2887.606 2446.961 3243.505

Imputation

## 
## INLA-IS
## 
## Posterior means:
## [1] 26.51511 28.39077 26.26560 22.03728 26.63045 27.00209 26.45522 26.49309
## [9] 26.59322
## 
## Posterior covariance:
##             [,1]        [,2]       [,3]       [,4]        [,5]       [,6]
##  [1,] 71.0397200 -0.90698063 -2.8133053  0.0326676  1.56609937  1.7629186
##  [2,] -0.9069806 33.50439599 -0.4254917 -1.4916191 -0.26614125 -0.2938505
##  [3,] -2.8133053 -0.42549170 65.2925397  0.3148071 -2.49085355 -5.4279263
##  [4,]  0.0326676 -1.49161909  0.3148071 36.8018981 -1.06252575 -0.7205948
##  [5,]  1.5660994 -0.26614125 -2.4908535 -1.0625257 74.81998516  1.2181388
##  [6,]  1.7629186 -0.29385050 -5.4279263 -0.7205948  1.21813881 65.6811630
##  [7,] -1.6296688  0.02653053  0.1897709 -0.1358322 -0.44410856  0.6933812
##  [8,] -0.0737553 -0.51698590  1.5222598 -3.1396391 -1.57803490 -0.7925197
##  [9,] -1.5093999 -0.66050618  1.2404515  0.9071227 -0.04322918  1.1478514
##              [,7]       [,8]        [,9]
##  [1,] -1.62966880 -0.0737553 -1.50939986
##  [2,]  0.02653053 -0.5169859 -0.66050618
##  [3,]  0.18977088  1.5222598  1.24045148
##  [4,] -0.13583225 -3.1396391  0.90712267
##  [5,] -0.44410856 -1.5780349 -0.04322918
##  [6,]  0.69338115 -0.7925197  1.14785139
##  [7,] 67.77608604  0.4406005  0.37192544
##  [8,]  0.44060051 70.5766706 -2.37564273
##  [9,]  0.37192544 -2.3756427 67.63923850
## 
## Sample size (to estimate the mean)
## [1] 3100.308
## 
## Sample size (to estimate the variance)
## [1] 121.7308
## 
## Sample size (to estimate the kurtosis)
## [1] 224.2479
## 
## L2 discrepancy
## [1] 0.01491806
## 
## Sample size (per variable)
## [1] 2839.153 2891.262 2686.612 3027.797 2579.964 3105.985 2778.729 3090.489
## [9] 2824.518
## 
## INLA-AMIS
## 
## Posterior means:
## [1] 26.46663 28.23594 26.63339 21.86560 26.62650 26.70178 26.38388 26.58096
## [9] 26.46127
## 
## Posterior covariance:
##             [,1]       [,2]       [,3]       [,4]        [,5]       [,6]
##  [1,] 71.5548043  0.4202454 -0.2931976  0.2243021  0.19380847  0.3500978
##  [2,]  0.4202454 30.5179421 -0.6198818 -1.5105641  1.04390174 -1.5939731
##  [3,] -0.2931976 -0.6198818 70.6144808  0.4178743 -0.88192054 -0.8256479
##  [4,]  0.2243021 -1.5105641  0.4178743 35.7855810 -0.67851751  0.1383889
##  [5,]  0.1938085  1.0439017 -0.8819205 -0.6785175 70.49588285  0.5968602
##  [6,]  0.3500978 -1.5939731 -0.8256479  0.1383889  0.59686018 69.7827746
##  [7,] -0.9864415 -0.1514551  0.2957732 -0.3499932 -0.95516741 -0.8938459
##  [8,]  0.4469601  0.2661267  0.5139215  0.8267749  0.04639142  0.3723948
##  [9,] -0.1513927 -0.7321365 -0.2532585  0.8814391 -0.52955914 -0.3175650
##             [,7]        [,8]       [,9]
##  [1,] -0.9864415  0.44696013 -0.1513927
##  [2,] -0.1514551  0.26612671 -0.7321365
##  [3,]  0.2957732  0.51392145 -0.2532585
##  [4,] -0.3499932  0.82677492  0.8814391
##  [5,] -0.9551674  0.04639142 -0.5295591
##  [6,] -0.8938459  0.37239477 -0.3175650
##  [7,] 70.7372096 -0.23780864  0.5304446
##  [8,] -0.2378086 70.89294968 -0.5518654
##  [9,]  0.5304446 -0.55186537 69.0829550
## 
## Sample size (to estimate the mean)
## [1] 9222.442
## 
## Sample size (to estimate the variance)
## [1] 5586.245
## 
## Sample size (to estimate the kurtosis)
## [1] 7123.592
## 
## L2 discrepancy
## [1] 0.002903645
## 
## Sample size (per variable)
## [1] 8270.826 8869.580 8433.700 8293.174 8468.784 8305.974 8178.022 8356.378
## [9] 8325.947

PQR

## 
## INLA-IS
## 
## Posterior means:
## [1]  13.65582 -10.18185
## 
## Posterior covariance:
##            [,1]       [,2]
## [1,]  0.3476949 -0.4383091
## [2,] -0.4383091  0.5693098
## 
## Sample size (to estimate the mean)
## [1] 1770.082
## 
## Sample size (to estimate the variance)
## [1] 356.7213
## 
## Sample size (to estimate the kurtosis)
## [1] 453.3711
## 
## L2 discrepancy
## [1] 0.0215626
## 
## Sample size (per variable)
## [1] 1657.741 1582.558
## 
## INLA-AMIS
## 
## Posterior means:
## [1]  13.67884 -10.20970
## 
## Posterior covariance:
##            [,1]       [,2]
## [1,]  0.3570757 -0.4491305
## [2,] -0.4491305  0.5812461
## 
## Sample size (to estimate the mean)
## [1] 6340.138
## 
## Sample size (to estimate the variance)
## [1] 5520.324
## 
## Sample size (to estimate the kurtosis)
## [1] 5711.095
## 
## L2 discrepancy
## [1] 0.007597714
## 
## Sample size (per variable)
## [1] 6312.414 6298.910